Although the simplest exact algorithm for TSP is O(n!), you can use dynamic programming to get the difficulty down to O(n^2 * 2^n), which is quite tractable at n=20.
However, sometimes you can construct exact solutions to much larger real-world data sets (tens of thousands of points) by exploiting structure in those graphs.
However, sometimes you can construct exact solutions to much larger real-world data sets (tens of thousands of points) by exploiting structure in those graphs.